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Article information
2008 , Volume 13, ¹ 6, p.40-49
Vitkovskiy V., Fedoruk M.P.
Numerical study of solutions of Schrodinger equation for laser pulses propagating in optical fibers
We present numerical simulations of nonlinear Schrodinger (NLS) equation with cubic nonlinearity for the Gauss and ring (m=1) initial spatial profiles. We determine a threshold power for the self-focusing collapse in a bulk dielectric medium and analyze solution properties that are independent of geometry of the experiment and the initial conditions. We observe oscillatory behaviour for different magnitudes near critical power and phase singularities. To approximate smooth solutions of this problem we construct special boundary conditions and implement a numerical algorithm based on a parallel sweep method for implicit Crank-Nicolson scheme. We then equip this scheme with an adaptive spatial and temporal mesh refinement mechanism that enables the numerical technique to correctly approximate singular solutions of the NLS equation. The calculations were performed using a high performance computer cluster allowing acceleration of 28 times over the sequential algorithm.
[full text]
Keywords: Numerical simulation, nonlinear Schrodinger equation, nonlinear physics, self focusing collaps, parallel algorithms
Author(s):
Vitkovskiy V.
Address: Russia, Novosibirsk
E-mail: wsiewolod@gmail.com
Fedoruk Mikhail Petrovich
Dr. , Academician RAS, Professor
Position: Chancellor
Office: Novosibirsk State University, Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, str. Pirogova, 2
Phone Office: (3832) 349105
E-mail: mife@net.ict.nsc.ru
SPIN-code: 4929-8753
Bibliography link:
Vitkovskiy V., Fedoruk M.P. Numerical study of solutions of Schrodinger equation for laser pulses propagating in optical fibers // Computational technologies. 2008. V. 13. ¹ 6. P. 40-49
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